Step-by-step state-selective tracking of fragmentation dynamics of water dications by momentum imaging

The double photoionization of a molecule by one photon ejects two electrons and typically creates an unstable dication. Observing the subsequent fragmentation products in coincidence can reveal a surprisingly detailed picture of the dynamics. Determining the time evolution and quantum mechanical states involved leads to deeper understanding of molecular dynamics. Here in a combined experimental and theoretical study, we unambiguously separate the sequential breakup via D+ + OD+ intermediates, from other processes leading to the same D+ + D+ + O final products of double ionization of water by a single photon. Moreover, we experimentally identify, separate, and follow step by step, two pathways involving the b 1Σ+ and a 1Δ electronic states of the intermediate OD+ ion. Our classical trajectory calculations on the relevant potential energy surfaces reproduce well the measured data and, combined with the experiment, enable the determination of the internal energy and angular momentum distribution of the OD+ intermediate.

As stated in the paper, our pathway separation method is simplified in practice by rotating Fig. 5 (from the paper) by 45 • , that is we plot in Fig. (a) the same data as a function of the KER difference and KER sum, namely KER diff = KER OD II ,D I -KER ODII and KER sum = KER OD II ,D I + KER ODII , respectively.
Next, we project Fig. (a) onto the KER sum axis, as shown in Fig. (b) (note that KER sum is the total kinetic energy release in the fragmentation process, denoted simply as KER).
Finally, we separate events larger than KER = 7.18 eV to one fragmentation pathway, 2 1 A 1 → b 1 Σ + , while events with smaller KER are associated with the other breakup pathway, 1 1 B 1 → a 1 ∆. , specifically the pathways are: 2 1 A 1 → b 1 Σ + (red) and 1 1 B 1 → a 1 ∆ (blue). Note that the overlap between the two distributions around the vertical line is small. Source data are provided as a Source Data file.
In Fig. 4 of the paper we compare the measured energy release, E release , following double ionization of heavy water by a 61-eV photon and leading to D + + D + + O threebody fragmentation, with the expected values. Recall that the measured E release is given by where KER is the total kinetic energy carried by the three massive fragments, and E e1 + E e2 is the kinetic energy of both electrons in the continuum. The measured spacing between the different dissociation limits associated with the oxygen 3 P ground state and the 1 D and 1 S excited states, match well the expected values, while matching the absolute values is more challenging. To circumvent such mismatch, it became common practice to show only the relative E release values, that is, the energy spacing when comparing measured spectrum and expected values [1].
To match our measured E release spectrum, shown in Fig. 4 of the paper, we have to downshift by 0.4 eV the expected value for the lowest dissociation limit, i.e., the D + + D + + O( 3 P) limit, denoted hereafter by the expression E[D + + D + + O( 3 P)]. It is important to note that this expected value is based on recommended measured values as explained below. The expected value of the energy release, denoted E ′ release to distinguish it from the measured value, is given by where E photon is the photon energy dialed in at the monochromator of the synchrotron beamline. Note that in this context we need to know the energy of the lowest As stated in the paper, the measured energy release, E release , associated with this dissociation limit is about 0.4 eV lower than the expected value, E ′ release . Though an absolute determination of this energy was not the goal in our experiment one may wonder what is the source for this mismatch. The scatter in the recommended values across measurements is of the order of 100 meV, i.e., much smaller than the shift. The uncertainties in our measurements originate from the calibration of the measured photon energy via indirect measurements [mostly angle-resolved photoemission spectroscopy (ARPES)]estimated to be 50-150 meV, the energy calibration of the electrons of about 50 meV (at around 20 eV), while the two ions contribute about 200 meV due to calibration using previous N 2 data [5]. Therefore, the absolute energy shift used in Fig. 4 is within the combined uncertainty of our measurement and the scatter in the recommended data.
In principle, though with significant effort, the uncertainties in our measurements can be reduced to enable accurate determination of the absolute energy. However, to identify the final states of the fragmentation process it is sufficient to use the relative energies (i.e., energy spacings between the peaks), and one would expect them to always be more precise, as they are independent of some of the systematic errors, like the accuracy of the beamline monochromator calibration or uncertainties in the dissociation energies.